Resampling methods such as the bootstrap are routinely used to esti- mate the ¯nite-sample null distributions of a range of test statistics. We present a simple and tractable way to perform classical hypothesis tests based upon a kernel estimate of the CDF of the bootstrap statistics. This approach has a number of appealing features: i) it can perform well when the number of bootstraps is ex- tremely small, ii) it is approximately exact, and iii) it can yield substantial power gains relative to the conventional approach. The proposed approach is likely to be useful when the statistic being bootstrapped is computationally expensive.